Robust Low-Rank Approximation of Data Matrices With Elementwise Contamination

RICARDO A. MARONNA; VÍCTOR J. YOHAI

TECHNOMETRICS

AMER STATISTICAL ASSOC

Año: 2008 vol. 50 p. 295 - 304

0040-1706

We propose a robust method to approximate an n × p data matrix with one of rank q. The method is based on Yohai´s regression MM estimates. It is intended to be resistant against the existence of both atypical rows and of scattered atypical cells and also to be able to cope with missing values. We propose an algorithm based on alternating M-regressions and a starting estimate based on successive rank-one fits, which involves O(npq) operations. Simulations show that our estimate outperforms competing estimates in terms of both efficiency and resistance. Three high-dimensional real data sets are analyzed. The running time of our estimate for large data sets is shown to be less than that of its competitorsWe propose a robust method to approximate an n × p data matrix with one of rank q. The method is based on Yohai´s regression MM estimates. It is intended to be resistant against the existence of both atypical rows and of scattered atypical cells and also to be able to cope with missing values. We propose an algorithm based on alternating M-regressions and a starting estimate based on successive rank-one fits, which involves O(npq) operations. Simulations show that our estimate outperforms competing estimates in terms of both efficiency and resistance. Three high-dimensional real data sets are analyzed. The running time of our estimate for large data sets is shown to be less than that of its competitors